。
She follows every latest fashion trend.
Literal
She [topic-は] fashion [of-の] latest [of-の] trend all [object-を] is-chasing.
Three nominal layers stacked with の: はやりの ('fashionable's') + 最新の ('newest's') + 傾向 ('tendency, trend') — 'fashion's newest trends.' Multi-の chains are common in Japanese and serve where English would use multiple adjectives or 'of' phrases. はやり derives from the verb 流行る ('to be popular, in vogue'); 流行 (りゅうこう) is the more formal Sino-Japanese partner. 追いかける is a compound verb (追う 'pursue' + かける 'apply, run') meaning 'chase, follow,' here used metaphorically for chasing trends.